7. MAGNETIC FIELDS IN HALOS

From observations of external galaxies, magnetic fields
are inferred in halos of spiral galaxies to distances of at
least 5 kpc and maybe even 10 kpc from the disk plane,
significantly beyond a synchrotron scale height (cf
Section 3.6).
Recently, dynamo models have directed some attention to
out-of-disk fields. Here we address the two logical
possibilities (while noting that they are not mutually exclusive): that
such fields are generated in situ in the halo or that they are generated
in the disk and then transported into the halo.

Interpretations of observations in the Milky Way suggest the presence
of turbulent velocities of at least 50 km s-1 in galactic
halos, compared to
estimates of 10 km s-1 in disks.
If we assume a length scale of order 0.5 kpc and that halo angular
velocities are
comparable with those in the disk, we get canonical estimates of
~ 3 km s-1
and t
~ 5 × 1027 cm2 s-1, to be compared
with
t ~
1026 cm2 s-1 in the disk.
[See, e.g. the discussion in
Poezd et al (1993).
Note that
Schultz et al (1994)
adopt halo turbulent velocities that are much
smaller than those in the disk: This may be a direct consequence of their
turbulence model with
<v2> /
z.]
Taking L ~ 10 kpc gives standard dynamo numbers
R =
L /
t ~
2 and R
= 0L2 /
t ~ 200.
These are large enough for a dynamo to be excited
(Ruzmaikin et al 1988a,
Section VIII.1;
Kahn & Brett 1993).
Note that such a dynamo would
operate in a quasi-spherical volume, rather than a thin disk, that
standard spherical
dynamos
preferentially excite fields of dipolar (A0) topology, and that these
are then often the only stable solutions of the full nonlinear equations. In
contrast, S0 fields are usually preferred in thin disks. This situation
immediately suggests the interesting possibility of simultaneous
excitation of dynamo fields of opposite parity types in the two subsystems
(halo and disk) (see
Sokoloff & Shukurov
1990).
A priori, the possible existence of magnetic structures
asymmetric with respect to the midplane, of neutral sheets, and of other
nonstandard phenomena cannot be dismissed, as has been shown in some
detail by
Brandenburg et al (1992).
Growth times in the halo are
substantially longer than in the disk, and the halo field may still be in a
transient state after a Hubble time. Detailed integrations show that,
starting from a seed field of mixed parity, the overall field is
initially dominated by S0 topology and concentrated in the disk.
This phase can persist for order
a Hubble time, but the final configuration is usually of A0 type,
and may even be oscillatory.
Given the long-lived transient phase with mixed parity fields present,
observers today may be presented not
with the eventual stable configuration, but rather an intermediate state
of quite arbitrary geometry.
Note that magnetic fields in the disk and halo of M51 are oppositely
directed (EM Berkhuijsen et al, in preparation): This argues for in situ
generation. More satisfactory halo models will need better data than is
currently available on the dependence of the angular velocity in the
halo on z, but these results seem qualitatively robust.
To summarize, in some circumstances, dynamo theory may not be able to
make detailed predictions about field geometries in specific galaxies.

A largely unexplored possibility is that some sort of Ponomarenko ("screw")
dynamo (e.g.
Ruzmaikin et al 1988c)
might operate in the halo, if large-scale quasi-radial outflows ("winds")
are twisted
into helical form by the galactic rotation. Such dynamos excite
nonaxisymmetric fields. If we take a simple model investigated by
Ruzmaikin et al and use their definitions, then a wind velocity of 100
km s-1 and a typical galactic angular
velocity gives a magnetic Reynolds number Rm large
enough for the dynamo to work. Naively, the
minimum e-folding time would be about 109 yr, but this
increases
as RM1/2 for larger Rm,
because the screw dynamo is "slow."
These estimates suggest that the mechanism might
be of marginal importance in halos, but real galaxy velocity fields are
likely to be less efficient dynamos than the idealized forms
considered by Ruzmaikin et al. We note in passing that
Spencer & Cram (1992)
have discussed models of field amplification
in which meridional flows ("winds") appear to play a central role. However,
they solve the problem purely in the disk region; moreover, their
solutions do not represent
dynamo generation but rather local compression of field and
hence the relevance to field generation processes in galaxies is unclear.